Hodge correlators

Hodge Correlators Ii

We define Hodge correlators for a compact Kähler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real mixed Hodge structure on the rational homotopy type of X. The Hodge correlators provide a canonical linear map from the cyclic homomogy of the cohomology algebra...

Hidden Hodge symmetries and Hodge correlators

l-adic Étale Theory Hodge Theory Category of l-adic Abelian category MHR Galois modules of real mixed Hodge strucrures Galois group Hodge Galois group GHod := Gal(Q/Q) Galois group of the category MHR Gal(Q/Q) acts on H∗ et(X,Ql), H∗(X(C),R) has a functorial where X is a variety over Q real mixed Hodge structure étale site ?? Gal(Q/Q) acts on the étale site, and thus ?? on categories of étale s...

Hodge Groups of Hodge Structures with Hodge Numbers

This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...

Hodge loci and absolute Hodge classes

On the Hodge Filtration of Hodge Modules

Let X be a complex manifold, and Z an irreducible closed analytic subset. We have the polarizable Hodge Module ICZQ H whose underlying perverse sheaf is the intersection complex ICZQ. See [16]. Let (M,F ) be its underlying filtered DX -Module. ThenM is the unique regular holonomic DX -Module which corresponds to ICZC by the Riemann-Hilbert correspondence [9] [13], and it is relatively easy to d...